While this article is actually a simple, rather old blog with no scientific or relieable proof, I think it does an excellent job of demonstrating the problems of a condorcet triple in real life situations. The case is three teams, (OU, Texas, and Texas Tech). Each team beat another of the teams (OU beat Texas Tech, Texas Tech beat Texas, and Texas beat OU). As a result of this system it is difficult to justify a ranking for the teams based on this. For example assuming OU is best because OU beat Texas Tech and Texas Tech beat Texas doesn't really hold, because OU itself lost to Texas (and you come up with similar resposne for all three attempts to 'appoint' a winner). This is a clear real life example of the problems of running int oa condorcet triple. I'm not exactly sure how these things are resolved in rankings, I feel like there are several other factors that play a role. However if OU were ranked first and I were Texas, I would still feel proud for beating the "number one" team. It puts an interesting thing on the topic for sure. I like how this clearly illustrates the dillemma of such a situation however and feel many people can relate and understand this sort of an explanation.

Looking back upon the trio of teams fighting for the number one ranking in college football, there was bound to be an argument no matter which team was ranked number one. One team was always going to have the chance to say that it beat the number one team. However, despite the fact that it's unfortunate that not all three teams can share the number one ranking or avoid a conflict, a number one team must be chosen. Therefore, certain methods like strength of schedule and total scores must be taken into account. For instance, Oklahoma crushed Texas Tech, which was the only blowout of the round robin of games played between Texas, Texas Tech, and Oklahoma. This naturally was the deciding factor for Oklahoma being crowned the number one team. In a voting situation, the condorcet method would be an interesting medium. If three candidates are running, the candidate that does not have a large following, but is fairly neutral, would probably win. In a head to head election with the majority holding candidates, the voters from the opposing side would vote for the neutral candidate. In this case, the neutral candidate would win the election. This method would apply well for sports such as college football, but in an election, the condorcet method would not be effective in choosing the best person for the job.

I think most rankings systems get rid of this "One team beat another, so it's better" logic. For example, the NBA ranks its teams very simply--according to the team's record. The only time when individual games matter is when home court advantage and seeding is decided in the playoffs. For example, if two teams have equal records, their divisional games are used in order to decide which team is "better" and deserves the higher seeding or home court advantage. However, since 82 games are played by each team every year, ties are not extremely common and it usually clear by a team's record which one is "better."

However, there are some sports like football where fewer games are played and each one can drastically change weekly rankings. One such sport is tennis. In tennis, because it is relatively common to fall and rise among the rankings, there are many times when a world's #1 player is beaten by a lower player. In fact, just last week, Nadal lost to #23-ranked Robin Soderling. In tennis, since upsets are common, the rankings are done in an entirely different way. A player that wins a tournament one year has the chance to "defend" the points he earned by winning the same tournament in the following year. I think this works for a sport like tennis for the top rankings, but among the lower rankings (25+) there is a lot of variation. If a lowly player wins a few tournaments, he can easily get into the top 50-100 and just as easily a player can drop out of the top 200 ranked players. If you're injured, the system works quickly to take away the points you earned and drop you out of the rankings quickly. I think this system works well for tennis.

In general, I think each sport has created its own ranking system that works well according to the frequency of the matches and the probability of an upset. The only gripes I would have in which maybe the condorcet system might be better is that in sports like football, basketball, and baseball, if a team makes a trade late in the season and start drastically improving, this may not be reflected in the rankings and can sometimes skew playoff seeding.

I've just posted about a similar topic regarding how the BCS ranking system works as a type of Borda count voting system. In the case of the BCS, the team with the best record is not necessarily regarded as the number 1 team. There are many other factors involved in the BCS ranking system, including schedule toughness and popularity is definitely an unspoken one as well.

Two sports that I believe have their rankings down well are the NBA and MLB. Both of these having ranking system is basically based on record, which usually seems to be the most fair option. The reason is works is because of the number of games each league plays, which allows a very good idea of what the skill and talent of that team. The NBA plays 82 while I believe the MLB plays 162. Barring early injuries and trades aside (not every voting system can take that into account) the large number of games gives a good indication of which teams are the best.

One of the good things that the MLB incorporated into their playoff choosing is the Wild Card. MLB is broken up into two leagues, American and National, which each having 3 conferences. The top teams from each conference gets into the playoffs plus the team with the best record overall in the Wild Card. The Wild Card looks at all other teams that are not first in their division, and the team at the top of this stack is included in the playoffs. This is really good for teams that play in a strong conference as they don't get punished for being up against such other good teams. A first place record in the NL West can be 70 wins, while the top two teams in the East may have 90 and 85 wins. Since the 85 win team is clearly better, it gets included in the playoffs.

As for Tennis, one clear example of how someone can lose their points quickly and drop out of the rankings is Maria Sharapova. At one point, Maria Sharapova was ranked #1 and before a 9 month injury she was ranked #9. After 9 months she came to the French Open this past week with a ranking above 100. She got through to the quarterfinals I believe and her ranking will greatly increase after the tournament. This system does work well for this, since their are a lot of tournaments that many players don't choose to enter, each tournament weighted differently in points. Obviously winning a Grand Slam is worth more than a small Open, and since many of the really talented players end up winning Grand Slams, they are ranked the highest. Another example is how Roger Federer was ranked #1 for over 200 weeks, winning a ton of tournaments. However, Rafael Nadal was able to overtake him after beating him in 4 major tournaments.